<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8">
    
    <title>numpy.random.Generator.noncentral_chisquare &mdash; NumPy v1.18 Manual</title>
    
    <link rel="stylesheet" type="text/css" href="../../../_static/css/spc-bootstrap.css">
    <link rel="stylesheet" type="text/css" href="../../../_static/css/spc-extend.css">
    <link rel="stylesheet" href="../../../_static/scipy.css" type="text/css" >
    <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" >
    <link rel="stylesheet" href="../../../_static/graphviz.css" type="text/css" >
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../../../',
        VERSION:     '1.18.1',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  false
      };
    </script>
    <script type="text/javascript" src="../../../_static/jquery.js"></script>
    <script type="text/javascript" src="../../../_static/underscore.js"></script>
    <script type="text/javascript" src="../../../_static/doctools.js"></script>
    <script type="text/javascript" src="../../../_static/language_data.js"></script>
    <script type="text/javascript" src="../../../_static/js/copybutton.js"></script>
    <link rel="author" title="About these documents" href="../../../about.html" >
    <link rel="index" title="Index" href="../../../genindex.html" >
    <link rel="search" title="Search" href="../../../search.html" >
    <link rel="top" title="NumPy v1.18 Manual" href="../../../index.html" >
    <link rel="up" title="Random Generator" href="../generator.html" >
    <link rel="next" title="numpy.random.Generator.noncentral_f" href="numpy.random.Generator.noncentral_f.html" >
    <link rel="prev" title="numpy.random.Generator.negative_binomial" href="numpy.random.Generator.negative_binomial.html" > 
  </head>
  <body>
<div class="container">
  <div class="top-scipy-org-logo-header" style="background-color: #a2bae8;">
    <a href="../../../index.html">
      <img border=0 alt="NumPy" src="../../../_static/numpy_logo.png"></a>
    </div>
  </div>
</div>


    <div class="container">
      <div class="main">
        
	<div class="row-fluid">
	  <div class="span12">
	    <div class="spc-navbar">
              
    <ul class="nav nav-pills pull-left">
        <li class="active"><a href="https://numpy.org/">NumPy.org</a></li>
        <li class="active"><a href="https://numpy.org/doc">Docs</a></li>
        
        <li class="active"><a href="../../../index.html">NumPy v1.18 Manual</a></li>
        

          <li class="active"><a href="../../index.html" >NumPy Reference</a></li>
          <li class="active"><a href="../../routines.html" >Routines</a></li>
          <li class="active"><a href="../index.html" >Random sampling (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.random</span></code>)</a></li>
          <li class="active"><a href="../generator.html" accesskey="U">Random Generator</a></li> 
    </ul>
              
              
    <ul class="nav nav-pills pull-right">
      <li class="active">
        <a href="../../../genindex.html" title="General Index"
           accesskey="I">index</a>
      </li>
      <li class="active">
        <a href="numpy.random.Generator.noncentral_f.html" title="numpy.random.Generator.noncentral_f"
           accesskey="N">next</a>
      </li>
      <li class="active">
        <a href="numpy.random.Generator.negative_binomial.html" title="numpy.random.Generator.negative_binomial"
           accesskey="P">previous</a>
      </li>
    </ul>
              
	    </div>
	  </div>
	</div>
        

	<div class="row-fluid">
      <div class="spc-rightsidebar span3">
        <div class="sphinxsidebarwrapper">
  <h4>Previous topic</h4>
  <p class="topless"><a href="numpy.random.Generator.negative_binomial.html"
                        title="previous chapter">numpy.random.Generator.negative_binomial</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="numpy.random.Generator.noncentral_f.html"
                        title="next chapter">numpy.random.Generator.noncentral_f</a></p>
<div id="searchbox" style="display: none" role="search">
  <h4>Quick search</h4>
    <div>
    <form class="search" action="../../../search.html" method="get">
      <input type="text" style="width: inherit;" name="q" />
      <input type="submit" value="search" />
      <input type="hidden" name="check_keywords" value="yes" />
      <input type="hidden" name="area" value="default" />
    </form>
    </div>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
        </div>
      </div>
          <div class="span9">
            
        <div class="bodywrapper">
          <div class="body" id="spc-section-body">
            
  <div class="section" id="numpy-random-generator-noncentral-chisquare">
<h1>numpy.random.Generator.noncentral_chisquare<a class="headerlink" href="#numpy-random-generator-noncentral-chisquare" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.Generator.noncentral_chisquare">
<code class="sig-prename descclassname">Generator.</code><code class="sig-name descname">noncentral_chisquare</code><span class="sig-paren">(</span><em class="sig-param">df</em>, <em class="sig-param">nonc</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.noncentral_chisquare" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from a noncentral chi-square distribution.</p>
<p>The noncentral <img class="math" src="../../../_images/math/1cbe49dd16598c0550b8a7477dd597e6bc04367e.svg" alt="\chi^2"/> distribution is a generalization of
the <img class="math" src="../../../_images/math/1cbe49dd16598c0550b8a7477dd597e6bc04367e.svg" alt="\chi^2"/> distribution.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>df</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Degrees of freedom, must be &gt; 0.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 1.10.0: </span>Earlier NumPy versions required dfnum &gt; 1.</p>
</div>
</dd>
<dt><strong>nonc</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Non-centrality, must be non-negative.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">df</span></code> and <code class="docutils literal notranslate"><span class="pre">nonc</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(df,</span> <span class="pre">nonc).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized noncentral chi-square distribution.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The probability density function for the noncentral Chi-square
distribution is</p>
<div class="math">
<p><img src="../../../_images/math/fcdb5a79d05ca47e037a7138f7ba83c662f05d50.svg" alt="P(x;df,nonc) = \sum^{\infty}_{i=0}
\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}
P_{Y_{df+2i}}(x),"/></p>
</div><p>where <img class="math" src="../../../_images/math/72e92add7b5b6a5a8aaec682ec6f7cfa75c44750.svg" alt="Y_{q}"/> is the Chi-square with q degrees of freedom.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="re3e5c8554f6d-1"><span class="brackets">1</span></dt>
<dd><p>Wikipedia, “Noncentral chi-squared distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution">https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Draw values from the distribution and plot the histogram</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">values</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span>                  <span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-Generator-noncentral_chisquare-1_00_00.png" src="../../../_images/numpy-random-Generator-noncentral_chisquare-1_00_00.png" />
</div>
<p>Draw values from a noncentral chisquare with very small noncentrality,
and compare to a chisquare.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">values</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="o">.</span><span class="mi">0000001</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span>                  <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">),</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">values2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span>                   <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">),</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">values</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">values2</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;ob&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-Generator-noncentral_chisquare-1_01_00.png" src="../../../_images/numpy-random-Generator-noncentral_chisquare-1_01_00.png" />
</div>
<p>Demonstrate how large values of non-centrality lead to a more symmetric
distribution.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">values</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span>                  <span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-Generator-noncentral_chisquare-1_02_00.png" src="../../../_images/numpy-random-Generator-noncentral_chisquare-1_02_00.png" />
</div>
</dd></dl>

</div>


          </div>
        </div>
          </div>
        </div>
      </div>
    </div>

    <div class="container container-navbar-bottom">
      <div class="spc-navbar">
        
      </div>
    </div>
    <div class="container">
    <div class="footer">
    <div class="row-fluid">
    <ul class="inline pull-left">
      <li>
        &copy; Copyright 2008-2019, The SciPy community.
      </li>
      <li>
      Last updated on Feb 20, 2020.
      </li>
      <li>
      Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 2.4.2.
      </li>
    </ul>
    </div>
    </div>
    </div>
  </body>
</html>